One-loop renormalization of heavy-light currents

TL;DR

This paper computes one-loop renormalization factors for heavy-light currents using Fermilab formalism, providing results that interpolate between static and massless limits, and includes scale setting with tadpole improvement.

Contribution

It presents the first detailed calculation of mass-dependent renormalization factors for heavy-light bilinears with numerical results for Wilson and Sheikholeslami-Wohlert actions.

Findings

Results smoothly interpolate from static to massless limit.

Provides numerical renormalization factors for different actions.

Calculates Brodsky-Lepage-Mackenzie scale $q^*$ with tadpole improvement.

Abstract

We calculate the mass dependent renormalization factors of heavy-light bilinears at one-loop order of perturbation theory, when the heavy quark is treated with the Fermilab formalism. We present numerical results for the Wilson and Sheikholeslami-Wohlert actions, with and without tree-level rotation. We find that in both cases our results smoothly interpolate from the static limit to the massless limit. We also calculate the mass dependent Brodsky-Lepage-Mackenzie scale $q^*$, with and without tadpole-improvement.